Subtract. Simplify, if possible.
-$$\frac { 7 x y } { x ^ { 2 } - y ^ { 2 } } - \frac { x - y } { x + y }$$
A) $\frac { - x ^ { 2 } + 5 x y - y ^ { 2 } } { ( x + y ) ( x + y ) }$

B) $\frac { x ^ { 2 } + 5 x y + y ^ { 2 } } { ( x + y ) ( x - y ) }$

C) $\frac { x ^ { 2 } + 9 x y + y ^ { 2 } } { ( x + y ) ( x - y ) }$

D) $\frac { - x ^ { 2 } + 9 x y - y ^ { 2 } } { ( x + y ) ( x - y ) }$

Question

Subtract. Simplify, if possible.
-$$\frac { 7 x y } { x ^ { 2 } - y ^ { 2 } } - \frac { x - y } { x + y }$$
A) $\frac { - x ^ { 2 } + 5 x y - y ^ { 2 } } { ( x + y ) ( x + y ) }$

B) $\frac { x ^ { 2 } + 5 x y + y ^ { 2 } } { ( x + y ) ( x - y ) }$

C) $\frac { x ^ { 2 } + 9 x y + y ^ { 2 } } { ( x + y ) ( x - y ) }$

D) $\frac { - x ^ { 2 } + 9 x y - y ^ { 2 } } { ( x + y ) ( x - y ) }$

Quizplus · Accepted Answer

To subtract the fractions, we need a common denominator. The denominator of the first fraction is $x^2-y^2=(x+y)(x-y)$, so we will write the second fraction with that denominator:  $\frac{7xy}{x^2-y^2}-\frac{x-y}{x+y}=\frac{7xy}{(x+y)(x-y)}-\frac{(x-y)(x-y)}{(x+y)(x-y)}=\frac{7xy-(x-y)(x-y)}{(x+y)(x-y)}=\frac{7xy-(x^2-2xy+y^2)}{(x+y)(x-y)}$. Combining like terms, we have $\frac{-x^2+9xy-y^2}{(x+y)(x-y)}=\frac{-(x^2-9xy+y^2)}{(x+y)(x-y)}=\frac{- (x-y)(x-9y)}{(x+y)(x-y)}=\boxed{	extbf{(D)}}$. We can simplify further by canceling the $x-y$ terms, but this is not necessary to find the correct answer.

Subtract Simplify, If Possible 7xyx2−y2−x−yx+y\frac { 7 x y } { x ^ { 2 } - y ^ { 2 } } - \frac { x - y } { x + y }x2−y27xy​−x+yx−y​

Subtract Simplify, If Possible $\frac { 7 x y } { x ^ { 2 } - y ^ { 2 } } - \frac { x - y } { x + y }$